Abstract: For linear discrete systems,a design method of guaranteed performance predictive repetitive control under new performance indexes was proposed.To improve the tracking performance of linear discrete systems,a performance evaluation index was introduced.The area error system was constructed by using the difference operator,and the preview information was introduced to obtain the extended area error system containing the preview information of the target signal and the interference signal.The guaranteed predictive repetitive control problem was transformed into the stabilization problem of a class of linear discrete systems under the performance evaluation index.Furthermore,the stability conditions of discrete systems were obtained by using Lyapunov method,linear matrix inequality processing technique and guaranteed performance controller design method.On this basis,considering the unobservable state of the system,the observe-based guaranteed performance predictive repetitive control was further designed.Finally,numerical simulation was used to verify the effectiveness of the proposed method.

Key words: linear discrete system, area error, guaranteed preview repetitive control, observer, linear matrix inequality

摘要： 为了提高线性离散系统的跟踪性能,引入一种性能评价指标,利用差分算子构造出面积误差系统,引入预见信息获得包含目标信号和干扰信号预见信息的扩大面积误差系统,将保性能预见重复控制问题转化为一类线性离散系统在性能评价指标下的稳定化问题。利用Lyapunov方法和线性矩阵不等式处理技巧及保性能控制器的设计方法,得到离散系统的稳定性条件。在此基础上考虑到系统状态不可观测,进一步设计了基于观测器的保性能预见重复控制。最后,用数值仿真验证所提方法的有效性。

关键词: 线性离散系统, 面积误差, 保性能预见重复控制, 观测器, 线性矩阵不等式